An algebraic characterization of $k$--colorability

29 Sep 2020 · Flores Ramón, Kahrobaei Delaram, Koberda Thomas ·

We characterize $k$--colorability of a simplicial graph via the intrinsic algebraic structure of the associated right-angled Artin group. As a consequence, we show that a certain problem about the existence of homomorphisms from right-angled Artin groups to products of free groups is NP--complete.